what I have done
this is a Geometric progression therefore sum to infinity =

a=

r =
r =

substituting back into the equation I get

sum to infinity =

can someone please show me where I am going wrong, thanks.

You could probably use induction.

Apr 10th 2013, 07:18 AM

Gusbob

Re: series proof

I'll replace with for convenience.

Using the identity , your series may be rewritten as

.

Individually, these two sums are convergent geometric series (do you know why?). Calculate the sum for each term and add them up. I have verified that you do indeed get the desired result (after some algebraic manipulations), but I have no desire to type it out. You should be able to work it out yourself.

You may need to justify why you are able to break the sum into two infinite series, but this is a straightforward application of limit theorems since both your series converge.